Solve a-4/a(a+2)^2*a+2/a-4

$$\frac { a - 4 } { a ( a + 2 ) ^ { 2 } } \times \frac { a + 2 } { a - 4 }$$

Evaluate

$$\frac{1}{a\left(a+2\right)}$$

Solution Steps

Multiply \frac{a-4}{a\left(a+2\right)^{2}} times \frac{a+2}{a-4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(a-4\right)\left(a+2\right)}{a\left(a+2\right)^{2}\left(a-4\right)}$$

Cancel out \left(a-4\right)\left(a+2\right) in both numerator and denominator.

$$\frac{1}{a\left(a+2\right)}$$

Use the distributive property to multiply a by a+2.

$$\frac{1}{a^{2}+2a}$$

Expand

$$\frac{1}{a\left(a+2\right)}$$

Solution Steps

Multiply \frac{a-4}{a\left(a+2\right)^{2}} times \frac{a+2}{a-4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(a-4\right)\left(a+2\right)}{a\left(a+2\right)^{2}\left(a-4\right)}$$

Cancel out \left(a-4\right)\left(a+2\right) in both numerator and denominator.

$$\frac{1}{a\left(a+2\right)}$$

Use the distributive property to multiply a by a+2.

$$\frac{1}{a^{2}+2a}$$